The invention relates to a center which can be made of injection-molded plastic, which is substantially tubular and cylindrical in shape, designed to receive yarn wound in turns and which is intended to undergo various processing operations and in particular dyeing treatments using liquid dye which is introduced inside the center and which penetrates in a centrifugal direction through the turns of the yarn in order to dye it in the most uniform way possible; the spools of yarn wound on the centers are consequently inserted in suitable dyeing equipment in order to carry out the abovementioned operation. In the case of certain yarns especially, powerful tension develops in the yarn when it is wetted and heated which gives rise to high tightening forces being exerted on the center; for these reasons, it is advantageous for the center to be able to undergo a reduction in its diameter, i.e. in its transverse section, in order to reduce the forces exerted by the yarn and especially to make these forces substantially uniform even deep within the spool, so as to ensure that the mass of yarn wound in turns is dyed in a substantially uniform manner. Centers which allow this reduction in transverse section, i.e. in practical terms a reduction in diameter, are already known but these known centers have certain drawbacks and in particular a considerable reduction in the area through which the dyeing liquid can pass through the pervious walls of the center once it has undergone a reduction in diameter. A further drawback of known centers of this type is that the reduction in diameter often cannot be controlled and can give rise to an excessive undesired contraction which can lead to additional drawbacks.